IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p404-d1033785.html
   My bibliography  Save this article

Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation

Author

Listed:
  • Mohammed Alabedalhadi

    (Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan)

  • Mohammed Shqair

    (College of Science, Zarqa University, Zarqa 132222, Jordan)

  • Shrideh Al-Omari

    (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Ajloun 26816, Jordan)

  • Mohammed Al-Smadi

    (Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, United Arab Emirates
    College of Commerce and Business, Lusail University, Doha 122104, Qatar)

Abstract

In this work, the class of nonlinear complex fractional Kundu-Eckhaus equation is presented with a novel truncated M-fractional derivative. This model is significant and notable in quantum mechanics with good-natured physical characteristics. The motivation for this paper is to construct new solitary and kink wave solutions for the governing equation using the ansatz method. A complex-fractional transformation is applied to convert the fractional Kundu-Eckhaus equation into an ordinary differential equations system. The equilibria of the corresponding dynamical system will be presented to show the existence of traveling wave solutions for the governing model. A novel kink and solitary wave solutions of the governing model are realized by means of the proposed method. In order to gain insight into the underlying dynamics of the obtained solutions, some graphical representations are drawn. For more illustration, several numerical applications are given and analyzed graphically to demonstrate the ability and reliability of the method in dealing with various fractional engineering and physical problems.

Suggested Citation

  • Mohammed Alabedalhadi & Mohammed Shqair & Shrideh Al-Omari & Mohammed Al-Smadi, 2023. "Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:404-:d:1033785
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/404/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/404/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. F. Gómez-Aguilar & Dumitru Baleanu, 2017. "Schrödinger equation involving fractional operators with non-singular kernel," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 31(7), pages 752-761, May.
    2. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anwar Aldhafeeri & Muneerah Al Nuwairan, 2023. "Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative," Mathematics, MDPI, vol. 11(5), pages 1-14, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yüzbaşı, Şuayip & Yıldırım, Gamze, 2022. "A collocation method to solve the parabolic-type partial integro-differential equations via Pell–Lucas polynomials," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
    3. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Bentout, Soufiane & Djilali, Salih, 2023. "Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 926-956.
    5. Kamran Kamran & Zahir Shah & Poom Kumam & Nasser Aedh Alreshidi, 2020. "A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    6. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
    7. Djennadi, Smina & Shawagfeh, Nabil & Abu Arqub, Omar, 2021. "A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Hasan, Shatha & El-Ajou, Ahmad & Hadid, Samir & Al-Smadi, Mohammed & Momani, Shaher, 2020. "Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    9. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2021. "Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    12. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    13. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    14. Li, X.Y. & Wu, B.Y., 2020. "A new kernel functions based approach for solving 1-D interface problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    15. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    16. Saha Ray, S. & Singh, P., 2021. "Numerical solution of stochastic Itô-Volterra integral equation by using Shifted Jacobi operational matrix method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    17. Gao, Wei & Baskonus, Haci Mehmet, 2022. "Deeper investigation of modified epidemiological computer virus model containing the Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    19. Omar Abu Arqub & Mohamed S. Osman & Abdel-Haleem Abdel-Aty & Abdel-Baset A. Mohamed & Shaher Momani, 2020. "A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    20. Roul, Pradip & Prasad Goura, V.M.K., 2020. "A high order numerical method and its convergence for time-fractional fourth order partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 366(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:404-:d:1033785. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.